Melanie Barron

2022-08-10

Jeffrey Jordon

Expert2022-11-08Added 2605 answers

Subtract $49$ from both sides of the equation.

${x}^{2}=-49$

Take the specified root of both sides of the equation to eliminate the exponent on the left side.

$x=\pm \sqrt{-49}$

Simplify $\pm \sqrt{-49}$.

Rewrite $-49$ as $-1\left(49\right)$.

$x=\pm \sqrt{-1\left(49\right)}$

Rewrite $\sqrt{-1\left(49\right)}$ as $\sqrt{-1}\cdot \sqrt{49}$.

$x=\pm \sqrt{-1}\cdot \sqrt{49}$

Rewrite $\sqrt{-1}$ as $i$.

$x=\pm i\cdot \sqrt{49}$

Rewrite $49$ as $7}^{2$.

$x=\pm i\cdot \sqrt{{7}^{2}}$

Pull terms out from under the radical, assuming positive real numbers.

$x=\pm i\cdot 7$

Move $7$ to the left of $i$.

$x=\pm 7i$

The complete solution is the result of both the positive and negative portions of the solution.

First, use the positive value of the $\pm$ to find the first solution.

$x=7i$

Next, use the negative value of the $\pm$ to find the second solution.

$x=-7i$

The complete solution is the result of both the positive and negative portions of the solution.

$x=7i,-7i$

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